تقرير
New vector transport operators extending a Riemannian CG algorithm to generalized Stiefel manifold with low-rank applications
| العنوان: | New vector transport operators extending a Riemannian CG algorithm to generalized Stiefel manifold with low-rank applications |
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| المؤلفون: | Wang, Xuejie, Deng, Kangkang, Peng, Zheng, Yan, Chengcheng |
| سنة النشر: | 2023 |
| المجموعة: | Computer Science Mathematics |
| مصطلحات موضوعية: | Mathematics - Optimization and Control, Mathematics - Numerical Analysis, 90C26, 90C30, 90C15, 90C06, 90C90 |
| الوصف: | This paper proposes two innovative vector transport operators, leveraging the Cayley transform, for the generalized Stiefel manifold embedded with a non-standard metric. Specifically, it introduces the differentiated retraction and an approximation of the Cayley transform to the differentiated matrix exponential. These vector transports are demonstrated to satisfy the Ring-Wirth non-expansive condition under non-standard metrics, and one of them is also isometric. Building upon the novel vector transport operators, we extend the modified Polak-Ribi$\grave{e}$re-Polyak (PRP) conjugate gradient method to the generalized Stiefel manifold. Under a non-monotone line search condition, we prove our algorithm globally converges to a stationary point. The efficiency of the proposed vector transport operators is empirically validated through numerical experiments involving generalized eigenvalue problems and canonical correlation analysis. |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1016/j.cam.2024.116024 |
| URL الوصول: | http://arxiv.org/abs/2311.00907 |
| رقم الأكسشن: | edsarx.2311.00907 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1016/j.cam.2024.116024 |
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